rules‚ chain rule‚ implicit differentiation‚ higher derivatives‚ differentials. 4. Mean value theorem: Mean value theorem of differentials‚ L`hospital rule‚ Taylor formula. 5. Infinite integrals: Antiderivatives and infinite integrals‚ substitution rule‚ integration by parts. 6. Definite integrals: Definition and properties of definite integral‚ criteria of existence of definite integrals‚ fundamental theorem of calculus‚ substitution rule‚ integration by parts‚ improper integrals. 7. Applications
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Objective To prove Distance formula = by experimentally Pre-knowledge We know Pythagoras Theorem Area of triangle Some Knowledge about coordinate Rules for signs of Co-ordinates Axes of Co-ordinates Geometrical Representation of quadratic polynomials Material Required Coloured Glazed paper Pair of scissors Geometry box Graph paper Drawing sheet Colour stick Pencil colour Fevistick/ Gum Procedure Let two points P(x1‚y1) and Q(x2‚y2) on graph sheet. And draw a set of perpendicular
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left translation of units to vertically up translation of units to vertically down reflection in y-axis reflection in x-axis scaling along y-axis by factor scaling along x-axis by factor Chapter 1: Limits & Continuity If‚ then Squeeze Theorem Suppose‚ if‚ then If‚ then and Chapter 2: Derivatives Function Derivative Constant Rule Constant Multiple Rule Sum Rule Product Rule Quotient Rule Chain Rule / Composite Implicit Differentiation Inverse Functions
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Name: ________________________ Class: ___________________ Date: __________ ID: A Ch 5 Review Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Find the value of x. The diagram is not to scale. a. ____ 32 b. 50 c. 64 d. 80 2. B is the midpoint of AC‚ D is the midpoint of CE‚ and AE = 11. Find BD. The diagram is not to scale. a. 5.5 b. 11 c. 1 22 d. 4.5 Name: ________________________ ____ 3. Points B‚ D‚ and F are midpoints
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QUIZ 1. She hid candles in her shoes so she could study math at night. Sonya Kovalevsky 2. He was a Greek mathematician whose school got burned down. Pythagorus 3. He was a Greek mathematician known for shouting “Eureka!” in his bathtub. Archimedes 4. Her bedroom wall was covered with calculus notes. Sonya Kovalevsky 5. This German mathematician was a smart child who went to college at age 14. Johann Carl Gauss 6. He was an English mathematician who was born on Christmas Day. Isaac Newton 7. He dropped
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trip from Chicago to Gutshot. The setting affects the characters because it is where Colin eventually will eventually get a job with Hassan‚ find a girlfriend (not named Katherine) and where he will in general become happier again and finish his theorem(explained later). After going on a tour to see Archduke Franz Ferdinand’s body guided by soon-to-be friend Lindsey Lee Wells‚ they are invited by Lindsey’s mom Hollis back to their house for dinner. After eating‚ Both Hassan and Colin are invited
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years old‚ he obtained a copy of George Shoobridge Carr’s Synopsis of Elementary Results in Pure and Applied Mathematics‚ 2 vol. (1880–86). This collection of some 6‚000 theorems (none of the material was newer than 1860) aroused his genius. Having verified the results in Carr’s book‚ Ramanujan went beyond it‚ developing his own theorems and ideas. In 1903 he secured a scholarship to the University of Madras but lost it the following year because he neglected all other studies in pursuit of mathematics
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popoasdfghjklhjv xcvbnm yfkhfhjg fghjf ghjf ghf gTheory is a contemplative and rational type of abstract or generalizing thinking‚ or the results of such thinking. Depending on the context‚ the results might for example include generalized explanations of how nature works. The word has its roots in ancient Greek‚ but in modern use it has taken on several different related meanings. A theory is not the same as a hypothesis. A theory provides an explanatory framework for some observation‚ and from
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2.1 Cantilever: Plot the load vs. deflection curve using below. From the load deflection curve‚ the modulus of the linear section can be found as: Load (N) vs. De.lection (m) 100 90 80 70 60 50 40 30 20 Load (N) vs. De8lection (m) 10 0 0 0.00064 0.00121 0.00176 0.00229 0.00255 0.00289 0.00325 0.00428
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Phytagoras was born in 570 BC‚ on the island of Samos‚ in the Ionian region. Pythagoras was the most recognized Greek mathematician and philosopher through his theorem. Known as "Father of Numbers"‚ he made an important contribution to philosophy and religious teaching in the late 6th century BC. His life and teachings are not so obvious as there are many legends and artificial tales about him. In Greek tradition‚ it is said that he traveled a lot‚ including to Egypt. Phytagoras’s journey to
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